Use when expressing the relief after eliminating a stressful problem. He finally got the monkey off his back by quitting the stressful job.
Pro Tip 2/3
Emotional Weight
Highlights the emotional burden associated with the problem that's been resolved. Clearing her debts, she got the monkey off her back.
Pro Tip 3/3
Persisting Difficulty
Implies the problem solved has been persistent, maybe spanning a long period. After years of study, he finally got the monkey off his back and graduated.